[When I gave a draft of part 3 to a friend to read, they commented on the first paragraph, “Math isn’t about giving things funny names; it’s about giving things meaningless names!” I had a thought on this topic but when I wrote part 3, but I couldn’t really make it fit and thought it wasn’t that interesting anyway, but my friend said it was, so here goes. (Parts 1, 2, 3.)]

15-year old Nino had an idea once: “Math is stupid! When solving physics problems, you always have to take the actual physical quantities, then make up weird letters to put them through the equations, and then you have to translate them back to the physical quantities. This makes it harder to see what you’re doing because, when you glance at an equation, you only see the relations between letters and not the relationships between the actual physical quantities. In the hundreds of years that science has been around, someone must’ve come up with a more intuitive way to write equations. After all, computer scientists don’t just call their variables a, b, c, x, y, z either!”

[Part 3 is about communicating mathematical ideas. Part 1, Part 2. I took care to contain the tedious math bits in single paragraphs, so the point is still clear if you choose to only read the fun parts.1]

summary. There is no such thing as “wrong” notation. All that counts is that you get the math right and communicate your ideas clearly.

Last time I explained how it’s not accurate to say that an electron “is” a wave function, because an electron is a thing in the universe and a wave function is a mathematical object, and mathematical objects don’t live in the real universe. When people talk about wave functions, they often use the letter $\psi$. Obviously, even though it looks all nice and wavy, the $\psi$ itself isn’t the wave function either – it’s just its name. The concept of names is one we know and love from the real world: When I point at a chair and say, “This is Bob,” it’ll be clear what I mean when I explain that Bob has three legs. While it’s a terrible idea to call a chair Bob, giving things and their relationships with each other funny names is basically what mathematics is all about.

In the future, when I have a list of my most notable essays, this one will be “The Long, Confusing, Meandering One.” This is my A Feast For Crows in terms of exciting action; it’s my American Gods in terms of quickly getting to the point; it’s my Getting Things Done in terms of elegant phrasing – you get the idea. Think of this more as a piece of performance art, rather than an informative article. ↩

In science, we try to understand the world by building models and theories that describe it. You see an apple falling on your head, think, “oh, maybe that’s how the planets move, too”, and you write down rules that allow for the motion of planets and don’t allow for some phenomena you do not see, like things falling upward. You call the collection of those rules your model, or theory. When you have your model, you perform more experiments to test it, and every time your model’s prediction roughly matches your observations, you get more confident that your model is correct.

[Part 1 is about a feeling about the world. Epistemic state: Maybe I shouldn’t commit to writing blog posts about every thought that occurs to me while browsing Wikipedia. Part 2, part 3.]

I decided I don’t like the term “laws of physics” to describe the way reality behaves. Calling them laws makes them sound optional1. Like, it would be really good if you didn’t break them because they are being enforced by the space police, but if you’re really clever, you can outrun the space police and break them anyway. But you can’t.

Weellll, this is arguably inaccurate, but the point is less about the terminology and more about the intuition, so whatev. ↩

[Kinda sappy and emotional in parts. Being posted sort of a long time after the event. Not totally happy with the way this post turned out, but, you know, better finished and mediocre than perfect and imaginary, or something. Epistemic state: I deleted a lot of “as far as I can tell”s. Just pretend like every sentence ends with those words, and please do tell me if I’m wrong about anything.]

I attended this year’s European LessWrong Community Weekend. The initial draft of this post began thus:

This is the event report I did not want to write and you do not want to read.

I decided I didn’t like this approach. During the Weekend, people always said, “make it your own.” So let’s do that instead.